Long only 1/n portfolio

import pandas as pd
pd.options.plotting.backend = "plotly"

import yfinance as yf

from cvx.simulator.builder import builder
from cvx.simulator.grid import resample_index

data = yf.download(tickers = "SPY AAPL GOOG MSFT",  # list of tickers
                   period = "10y",                   # time period
                   interval = "1d",                 # trading interval
                   prepost = False,                 # download pre/post market hours data?
                   repair = True)                   # repair obvious price errors e.g. 100x?

[                       0%                       ]

[**********************50%                       ]  2 of 4 completed

[**********************75%***********            ]  3 of 4 completed
[*********************100%***********************]  4 of 4 completed

prices = data["Adj Close"]

capital = 1e6

b = builder(prices=prices, initial_cash=capital)

for time, state in b:
    # each day we invest a quarter of the capital in the assets
    b[time[-1]] = 0.25 * state.nav / state.prices

portfolio = b.build()
portfolio.profit.cumsum().plot()

portfolio.nav.plot()

Rebalancing

Usually we would not execute on a daily basis but rather rebalance every week, month or quarter. There are two approaches to deal with this problem in cvxsimulator.

• Resample the existing daily portfolio (helpful to see effect of your hesitated trading)

• Trade only on days that are within a predefined grid (most flexible if you have a rather irregular grid)

Resample an existing portfolio

portfolio_resampled = portfolio.resample(rule="M")

frame = pd.DataFrame({"original": portfolio.nav, "monthly": portfolio_resampled.nav})
frame

	original	monthly
Date
2013-08-15	1.000000e+06	1.000000e+06
2013-08-16	1.000672e+06	1.000672e+06
2013-08-19	1.001093e+06	1.001113e+06
2013-08-20	1.000803e+06	1.000723e+06
2013-08-21	1.000957e+06	1.000896e+06
...	...	...
2023-08-08	7.926160e+06	7.906738e+06
2023-08-09	7.846553e+06	7.826933e+06
2023-08-10	7.850001e+06	7.830541e+06
2023-08-11	7.837248e+06	7.817693e+06
2023-08-14	7.909948e+06	7.890452e+06

2516 rows × 2 columns

print(portfolio_resampled.stocks)

                    AAPL          GOOG         MSFT          SPY
Date                                                            
2013-08-15  16108.563696  11676.107389  9371.093873  1805.200529
2013-08-16  16108.563696  11676.107389  9371.093873  1805.200529
2013-08-19  16108.563696  11676.107389  9371.093873  1805.200529
2013-08-20  16108.563696  11676.107389  9371.093873  1805.200529
2013-08-21  16108.563696  11676.107389  9371.093873  1805.200529
...                  ...           ...          ...          ...
2023-08-08  10482.188116  15525.481048  6088.052888  4485.751044
2023-08-09  10482.188116  15525.481048  6088.052888  4485.751044
2023-08-10  10482.188116  15525.481048  6088.052888  4485.751044
2023-08-11  10482.188116  15525.481048  6088.052888  4485.751044
2023-08-14  10482.188116  15525.481048  6088.052888  4485.751044

[2516 rows x 4 columns]

# almost hard to see that difference between the original and resampled portfolio
frame.plot()

# number of shares traded
portfolio_resampled.trades_stocks.iloc[1:].plot()

Trade only days in predefined grid

b = builder(prices=prices, initial_cash=capital)

# define a grid
grid = resample_index(prices.index, rule="M")

for time, state in b:
    # each day we invest a quarter of the capital in the assets
    if time[-1] in grid:
        b[time[-1]] = 0.25 * state.nav / state.prices
    else:
        # forward fill an existing position
        b[time[-1]] = b[time[-2]]
        
portfolio = b.build()

portfolio.nav.plot()

# Trading only once a month can lead to days where 150k had to be reallocated
portfolio.turnover.iloc[1:].plot()

Why not resampling the prices?

I don’t believe in bringing the prices to a monthly grid. This would render it hard to construct signals given the sparse grid. We stay on a daily grid and trade once a month.